Problem: N different natural numbers are given. If you select four different ones and set them as $ A $, $ B $, $ C $, $ D $, the following formula

$ \ Frac {A + B} {C --D} $



I want to find the maximum value of.




Given N different natural numbers, choose 4 different from them and create a program to find the maximum value of the above formula.



Input

The input is given in the following format.


N
a1 a2 ... aN


The number N (4 ≤ N ≤ 1000) of natural numbers is given in the first line. The value ai (1 ≤ ai ≤ 108) of each natural number is given in the second line. However, the same natural number does not appear more than once (ai ≠ aj for i ≠ j).

Output

Outputs the maximum value of the above formula as a real number for a given N natural numbers. However, the error must not exceed plus or minus 10-5.

Examples

Input

10
1 2 3 4 5 6 7 8 9 10


Output

19.00000


Input

5
22 100 42 3 86


Output

9.78947


Input

6
15 21 36 10 34 5


Output

18.00000


Input

4
100000 99999 8 1


Output

28571.285714

Solution (in CPP):

Solution:
#include<bits/stdc++.h>
using namespace std;
int n;
int a[10000];

double f(int A,int B,int C,int D){
  return (double)(a[A]+a[B])/(double)(a[C]-a[D]);
}

int main(){
  cin>>n;
  for(int i=0;i<n;i++)cin>>a[i];
  sort(a,a+n);
  reverse(a,a+n);
  double ans=max(f(2,3,0,1),f(0,3,1,2));
  for(int i=2;i+1<n;i++){
    ans=max(ans,f(0,1,i,i+1));
  }
  printf("%.10f\n",ans);
  return 0;
}